Renormalization Group Approaches to Quantum Gravity

The Renormalization Group provides a unifying tool to study quantum gravity approaches: Bridging the gap between microscopic and macroscopic scales, it can be used in two directions in quantum gravity: On the one hand, following the Renormalization Group flow towards high momentum scales allows us to test the consistency of the asymptotic safety scenario for quantum gravity. On the other hand, following the flow towards the infrared, allows us to check whether a viable semiclassical limit emerges from a microscopic model of quantum gravity, such as a spin foam model. Very much in the spirit of condensed-matter models, fixed points of the Renormalization Group flow can provide a continuum limit in approaches such as Causal Dynamical Triangulations, spin foams, matrix and tensor models.

This workshop will for the first time bring together researchers working on different models of quantum gravity, who use the Renormalization Group in different forms. We will discuss conceptual as well as more technical questions, and establish a new dialogue between different quantum gravity approaches.

What is the meaning of asymptotic freedom or asymptoticsafety in group space?

Bob Room

6:30pm

Casual Dinner – Details TBA

Offsite

Jan Ambjorn, Niels Bohr Institute

RG flow in CDT

An attempt is made to define "lines of contant physics" in CDT and relate the corresponding picture to non-trivial UV fixed points as they appear in the asymptotic safety scenario.

Benjamin Bahr, University of Hamburg

On background-independent renormalization in state-sum models

In this talk we discuss some notion of coarse graining in state-sums, most notably a class of spin foam models in their holonomy representations. We discuss the notion of scale in this context, and how diffeomorphism-invariance ties into the existence of a continuum limit. We close with an example and muse about the interplay between diffeomorphism-invariance and non-renormalizability.

Dario Benedetti, Albert Einstein Institute

One-loop renormalization in a toy model of Horava-Lifshitz gravity

I will present some recent results on the UV properties of a toy model of Horava-Lifshitz gravity in 2+1 dimensions. In particular, I will illustrate some details of a one-loopcalculation, leading to beta functions for the running couplings. The renormalization group flow obtained in such way shows that Newton's constant is asymptotically free. However, the DeWitt supermetric approaches its Weyl invariant form with the same speed and the effective interaction coupling of the scalar degree of freedom remains constant along the flow. I will discuss some general lesson that we can learn from these results.

Alfio Bonanno, INAF

Confronting Asymptotically Safe Inflation with Planck data

Sylvain Carrozza, CPT Marseille

Renormalization group approach to 3d group field theory

I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point. I will close with preliminary investigations about the existence of a non-trivial fixed point.

Joshua Cooperman, Radboud University Nijmegen

Renormalization of entanglement entropy and the gravitational effective action

The entanglement entropy associated with a spatial boundary in quantum field theory is ultraviolet divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I argue that the Callan-Wilczek prescription is rigorously justified at least for a particular class of quantum states each expressible as a Euclidean path integral. I then show that the entanglement entropy is rendered ultraviolet finite by precisely the counterterms required to cancel the ultraviolet divergences in the gravitational effective action. In particular, the leading contribution to the entanglement entropy is given by the renormalized Bekenstein-Hawking formula. These results apply to a general quantum field theory coupled to a fixed background metric, holding for arbitrary entangling surfaces with vanishing extrinsic curvature in any dimension, to all orders in perturbation theory in the quantum fields, and for all ultraviolet divergent terms in the entanglement entropy. I also reconcile these results on the entanglement entropy with the existing literature, compare them to the Wald entropy, and speculate on their interpretation and implication.

Bianca Dittrich, Perimeter Institute

Quantum Spacetime Engineering

Given (a set of) fundamental models of quantum space time, for instance spin foam models, we aim to understand the large scale physics encoded in these fundamental models. Renormalization and coarse graining address this issue and help to understand how large scale physics depends on parameters in the fundamental models.

I will review recent work on coarse graining and renormalization of spin foam and analogue models, revealing possible large scale phases, depending on parameters of the microscopic models. I will explain how these phases are connected to topological field theories and possible vacua for the theory of quantum gravity, e.g. loop quantum gravity. I outline how these different vacua are connected to different representations of the observable algebra, that is different Hilbert spaces, and how this allows to expand the theory around different vacuum states.

John Donoghue, University of Massachusetts

Perturbative quantum gravity calculations and running couplings

We know how to make perturbative calculations in quantum gravity using the framework of effective field theory. I will describe the basics of the effective field theory treatment and look at several calculations. There are obstacles to describing these with running coupling constants. Finally, I will do my best to try to connect these with the Asymptotic Safety program.

Astrid Eichhorn, Perimeter Institute

Why matter matters in quantum gravity

I will argue that a fundamental theory of quantum gravity that is applicable to our universe must include matter degrees of freedom. In my talk I will focus on the option that these are fundamental, in contrast to low-energy effective, degrees of freedom, and must thus be included in the microscopic dynamics of spacetime.I will present evidence that dynamical Standard Model matter is compatible with asymptotically safe quantum gravity, while several "Beyond Standard Model" scenarios are disfavored. I will also discuss how the coupling to matter opens a window into the observational quantum gravity regime.

Recently, the development of tensor network renormalization approach has provided us a powerful tool to construct new classes of topological quantum field theories(TQFTs) in discrete space-time. For example, the Turaev Viro’s states sum constructions are fixed point tensor networks representing a special class of 2+1D TQFTs. Interestingly, the Grassmann variable generalization of tensor network renormalization approach leads to new classes of TQFTs for interacting fermion systems, namely, the fermionic TQFTs. In this talk, I will start with a fermionic topological nonlinear sigma model and discuss its corresponding new mathematics - group super-cohomology theory. Then I will explain the fermionic generalization of Dijkgraaf -Witten gauge theory by using group supercohomology theory. Finally I will show examples beyond fermionic Dijkgraaf -Witten gauge theory and discuss possible new routes towards quantum gravity.

Razvan Gurau, Université Paris-Sud XI Orsay

Tensor Models in the Large N limit

Tensor models generalize matrix models and provide a framework for the study of random geometries in arbitrary dimensions. Like matrix models they support a 1/N expansion, where N is the size of the tensor, with an analytically controlled large N limit. In this talk I will present some recent results in this field and I will discuss their implications for quantum gravity.

Petr Horava, University of California, Berkeley

Phases of Gravity

Quantum gravity with anisotropic scaling exhibits a rich structure of phases and phase transitions, dominated by multicritical behavior dependent on the spacetime dimension and the dynamical critical exponent. I will discuss some features of this phase structure, as well as its similarities and differences in comparison to the CDT approach to quantum gravity.

Tim Koslowski, University of New Brunswick

Asymptotic safety in a pure matrix model

The connection between two-dimensional Euclidean gravity and pure matrix models has lead to may fundamental insights about quantum gravity and string theory. The pure matrix model is thus a blueprint for the connection between discrete models and Euclidean quantum gravity. I will report on work with Astrid Eichhorn in which this "blueprint" model is investigated with the functional renormalization group. In this model, I will discuss the questions: "What is a possible meaning of asymptotic safety in a discrete model?" and "Is it possible to apply the FRGE to tensor models?

Daniel Litim, University of Sussex

Lessons from asymptotic safety

Two aspects of asymptotic safety are highlighted. First, I discuss how asymptotic safety can be tested with the help of a bootstrap strategy. This is then applied to high-order polynomial actions of the Ricci scalar and beyond. Second, I discuss how phenomenological signatures of asymptotic safety can be searched for at particle colliders such as the LHC, provided that the quantum gravity scale is in the TeV energy regime.

Renate Loll, Radboud University Nijmegen

What you always wanted to know about CDT, but did not have time to read about in our papers

I will review the approach of Causal Dynamical Triangulations to nonperturbative quantum gravity, high-lighting some frequently mis- or ununderstood features, emphasizing recent developments and discussing some interesting open issues.

Mercedes Martin-Benito, Radboud University Nijmegen

Refinement limit of quantum group spinnets

The many-building-blocks limit of spin foam models remains to be an open question. The complexity of these models makes the analysis of their possible continuum phases a very difficult task. In the last years progress in this direction has been made by considering simplified, yet featured-rich, analog models to spin foams, the so-called spin net models. These models retain the main dynamical ingredient of spin foams, namely the simplicity constraints. In this talk we will introduce spin net models based on the quantum group SU(2)_q, and we will review the use of tensor network renormalization group techniques to study their coarse graining. We will analyze the resulting phase diagram, which interestingly displays a rich structure of fixed points. Furthermore we will discuss the relation of spin nets with spin foams.

Tim Morris, University of Southampton

Recent developments in asymptotic safety: tests and properties

The talk will review recent tests of the asymptotic safety conjecture within functional renormalisation group studies and progress in understanding the properties that such a fixed point would have.

Daniele Oriti, Albert Einstein Institute

Renormalization of group field theories: motivations and a brief review

Group field theories are tensorial models enriched with group-theoretic data in order to define proper field theories of quantum geometry. They can be understood as a second quantised (Fock space) reformulation of loop quantum gravity kinematics and dynamics. The renormalization group provides, as a in any quantum field theory, a key tool to select well-defined models, to unravel the impact of quantum effects on the dynamics across different scales, and to study the continuum limit. Beside introducing the general formalism and clarifying the relation to other approaches, we will motivate the renormalisation group analysis of group field theories and review recent developments in this direction.

Jan Pawlowski, University of Heidelberg

Global flows in quantum gravity

In this talk I present recent work on complete UV-IR flows for the fully momentum-dependent propagator, RG-consistent vertices, Newtons coupling and the cosmological constant. For the first time, a global phase diagram is obtained where the non-Gaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to an infrared fixed point with classical scaling. Physics implications as well as the extension to gauge-matter-gravity systems are discussed.

Martin Reuter, Johannes Gutenberg-Universität Mainz

The Asymptotic Safety Program: new results and an inconvenient truth

We briefly review the various components and their conceptual status of the full Asymptotic Safety Program which aims at finding a nonperturbative infinite-cutoff limit of a regularized functional integral for a quantum field theory of gravity. It is explained why in the continuum formulation based on the Effective Average Action the key requirement of background independence unavoidably results in a "bi-metric" framework, and recent results on truncated RG flows of bi-metric actions are presented. They suggest that the next generation of truncations that must be explored should be of bi-metric type. As an application, a method of characterizing and counting physical states is shown to arise.

Vincent Rivasseau, Université Paris-Sud XI Orsay

Between Matrices and Tensors

Quartic tensor models can be rewritten in terms of intermediate matrix fields. The corresponding expansion is not only simpler, it suggests also new bridges between matrices, strings and tensors.

James Ryan, Albert Einstein Institute

Double scaling in tensor models

I present recent work on the double scaling limit of random tensor models through the analysis of their Schwinger-Dyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories.

Frank Saueressig, Radboud University Nijmegen

Gravitational RG flows on foliated spacetimes

The role of time and a possible foliation structure of spacetime are longstanding questions which lately received a lot of renewed attention from the quantum gravity community. In this talk, I will review recent progress in formulating a Wetterich-type functional renormalization group equation on foliated spacetimes and outline its potential applications. In particular, I will discuss first results concerning the RG flow of Horava-Lifshitz gravity, highlighting a possible mechanism for a dynamical Lorentz-symmetry restoration at low energies.

Kellogg Stelle, Imperial College, London

What happens to the Schrödinger solution in quantum corrected gravity?

I present recent work on the double scaling limit of random tensor models through the analysis of their Schwinger-Dyson equations. This study exemplifies their potential for probing the continuum phase structure of these theories.

I will start with a brief overview of tensorial group field theories with gauge invariant condition and their relation to spin foam models. The rest of the talk will be focused on the SU(2) theory in dimension 3, which is related to Euclidean 3d quantum gravity and has been proven renormalizable up to order 6 interactions. General renormalization group flow equations will be introduced, allowing in particular to understand the behavior of the relevant couplings in the neighborhood of the Gaussian fixed point.

The entanglement entropy associated with a spatial boundary in quantum field theory is ultraviolet divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I argue that the Callan-Wilczek prescription is rigorously justified at least for a particular class of quantum states each expressible as a Euclidean path integral.

I will argue that a fundamental theory of quantum gravity that is applicable to our universe must include matter degrees of freedom. In my talk I will focus on the option that these are fundamental, in contrast to low-energy effective, degrees of freedom, and must thus be included in the microscopic dynamics of spacetime.

We briefly review the various components and their conceptual status of the full Asymptotic Safety Program which aims at finding a nonperturbative infinite-cutoff limit of a regularized functional integral for a quantum field theory of gravity. It is explained why in the continuum formulation based on the Effective Average Action the key requirement of background independence unavoidably results in a "bi-metric" framework, and recent results on truncated RG flows of bi-metric actions are presented.

The role of time and a possible foliation structure of spacetime are longstanding questions which lately received a lot of renewed attention from the quantum gravity community. In this talk, I will review recent progress in formulating a Wetterich-type functional renormalization group equation on foliated spacetimes and outline its potential applications. In particular, I will discuss first results concerning the RG flow ofHorava-Lifshitz gravity, highlighting a possible mechanism for a dynamical Lorentz-symmetry restoration at low energies.

I will present some recent results on the UV properties of a toy model of Horava-Lifshitz gravity in 2+1 dimensions. In particular, I will illustrate some details of a one-loopcalculation, leading to beta functions for the running couplings. The renormalization group flow obtained in such way shows that Newton's constant is asymptotically free. However, the DeWitt

Quantum gravity with anisotropic scaling exhibits a rich structure of phases and phase transitions, dominated by multicritical behavior dependent on the spacetime dimension and the dynamical critical exponent. I will discuss some features of this phase structure, as well as its similarities and differences in comparison to the CDT approach to quantum gravity.

In this talk we discuss some notion of coarse graining in state-sums, most notably a class of spin foam models in their holonomy representations. We discuss the notion of scale in this context, and how diffeomorphism-invariance ties into the existence of a continuum limit. We close with an example and muse about the interplay between diffeomorphism-invariance and non-renormalizability.